DFS Depth First Search on Graph in DSA Rust - Build from Scratch

DFS Depth First Search on Graph

📖 Scenario: You are exploring a small map of connected cities. Each city is linked to some other cities by roads. You want to visit all cities starting from a specific city, going as deep as possible before backtracking. This is like exploring a maze by always going forward until you cannot go further, then stepping back.

🎯 Goal: Build a program that uses Depth First Search (DFS) to visit all cities in the map starting from city 0. You will create the graph, set up a visited list, write the DFS function, and print the order of cities visited.

📋 What You'll Learn

Create a graph as an adjacency list using a vector of vectors of usize

Create a vector called visited to track visited cities

Write a recursive DFS function named dfs that takes the graph, visited vector, and current city index

Print the order of cities visited during DFS

💡 Why This Matters

🌍 Real World

DFS is used in many real-world problems like maze solving, network traversal, and finding connected components.

💼 Career

Understanding DFS is essential for software engineers working on algorithms, game development, and systems programming.

1

Create the graph as an adjacency list

Create a variable called graph as a vector of vectors of usize with these exact connections: city 0 connects to cities 1 and 2, city 1 connects to city 2, city 2 connects to city 0 and 3, city 3 connects to city 3.

DSA Rust

# Your code here

Hint

Think of graph as a list where each city has a list of cities it connects to.

2

Create the visited vector

Create a mutable vector called visited of type Vec with length 4, initialized with false values.

DSA Rust

let graph: Vec> = vec![
    vec![1, 2],
    vec![2],
    vec![0, 3],
    vec![3],
];
# Your code here

Hint

This vector keeps track of which cities you have already visited.

3

Write the DFS function

Write a recursive function called dfs that takes graph: &Vec>, visited: &mut Vec, and city: usize. Inside, mark visited[city] as true. Then, for each neighbor in graph[city], if it is not visited, call dfs recursively on that neighbor. Print the current city inside the function after marking it visited.

DSA Rust

let graph: Vec> = vec![
    vec![1, 2],
    vec![2],
    vec![0, 3],
    vec![3],
];

let mut visited: Vec = vec![false; 4];

// Write the dfs function here
# Your code here

Hint

Mark the city visited, print it, then visit all neighbors recursively if not visited.

4

Call DFS and print the visit order

Call the dfs function with &graph, &mut visited, and starting city 0. This will print the order of cities visited.

DSA Rust

let graph: Vec> = vec![
    vec![1, 2],
    vec![2],
    vec![0, 3],
    vec![3],
];

let mut visited: Vec = vec![false; 4];

fn dfs(graph: &Vec>, visited: &mut Vec, city: usize) {
    visited[city] = true;
    println!("Visited city {}", city);
    for &neighbor in &graph[city] {
        if !visited[neighbor] {
            dfs(graph, visited, neighbor);
        }
    }
}

// Call dfs starting from city 0
# Your code here

Hint

Just call dfs(&graph, &mut visited, 0); to start visiting from city 0.

Practice

1. What is the main idea behind Depth First Search (DFS) on a graph?

easy

A. Explore as far as possible along each branch before backtracking

B. Visit all nodes at the current depth before moving deeper

C. Visit nodes randomly without any order

D. Only visit nodes with the highest value first

Solution

1. Step 1: Understand DFS traversal

   DFS explores a graph by going deep into one branch before exploring others.

2. Step 2: Compare with other traversal methods

   BFS visits nodes level by level, but DFS goes deep first.

3. Final Answer:

   Explore as far as possible along each branch before backtracking -> Option A

4. Quick Check:

   DFS = deep exploration first [OK]

Hint: DFS means go deep first, then backtrack [OK]

Common Mistakes:

• Confusing DFS with BFS
• Thinking DFS visits nodes level-wise
• Assuming DFS visits nodes randomly

2. Which of the following is the correct Rust function signature for a recursive DFS function on a graph represented as adjacency list?

easy

A. fn dfs(graph: &mut Vec, node: usize, visited: Vec<bool>)

B. fn dfs(graph: Vec, node: usize, visited: Vec<bool>)

C. fn dfs(graph: &Vec, node: usize, visited: &mut Vec<bool>)

D. fn dfs(graph: Vec, node: usize, visited: &mut Vec<bool>)

Solution

1. Step 1: Understand parameter passing in Rust for DFS

   The graph should be passed by reference to avoid copying, and visited vector should be mutable reference to mark nodes visited.

2. Step 2: Check each option

   fn dfs(graph: &Vec, node: usize, visited: &mut Vec<bool>) passes graph by reference and visited as mutable reference, which is correct for DFS recursion.

3. Final Answer:

   fn dfs(graph: &Vec, node: usize, visited: &mut Vec<bool>) -> Option C

4. Quick Check:

   Graph by ref + visited mutable ref = correct DFS signature [OK]

Hint: Pass graph by ref and visited as mutable ref [OK]

Common Mistakes:

• Passing graph or visited by value causing copies
• Not using mutable reference for visited
• Using mutable reference for graph unnecessarily

3. What is the output of the following Rust DFS traversal starting from node 0?

fn dfs(graph: &Vec, node: usize, visited: &mut Vec<bool>, result: &mut Vec<usize>) {
    visited[node] = true;
    result.push(node);
    for &neighbor in &graph[node] {
        if !visited[neighbor] {
            dfs(graph, neighbor, visited, result);
        }
    }
}

fn main() {
    let graph = vec![
        vec![1, 2],
        vec![0, 3],
        vec![0],
        vec![1]
    ];
    let mut visited = vec![false; 4];
    let mut result = Vec::new();
    dfs(&graph, 0, &mut visited, &mut result);
    println!("{:?}", result);
}

medium

A. [0, 2, 1, 3]

B. [0, 1, 3, 2]

C. [0, 1, 2, 3]

D. [1, 0, 2, 3]

Solution

1. Step 1: Trace DFS starting at node 0

   Start at 0, mark visited, add 0. Neighbors: 1, 2. Visit 1 first.

2. Step 2: Continue DFS from node 1

   Visit 1, add 1. Neighbors: 0 (visited), 3 (not visited). Visit 3 next.

3. Step 3: Visit node 3

   Visit 3, add 3. Neighbor: 1 (visited). Backtrack to 0 and visit 2.

4. Step 4: Visit node 2

   Visit 2, add 2. Neighbor: 0 (visited). DFS complete.

5. Final Answer:

   [0, 1, 3, 2] -> Option B

6. Quick Check:

   DFS order from 0 = [0,1,3,2] [OK]

Hint: Follow neighbors in order, mark visited, backtrack [OK]

Common Mistakes:

• Visiting neighbors out of order
• Not marking visited nodes
• Confusing BFS order with DFS

4. Identify the bug in this DFS Rust code snippet and choose the fix:

fn dfs(graph: &Vec, node: usize, visited: &mut Vec<bool>) {
    visited[node] = true;
    for neighbor in &graph[node] {
        if visited[*neighbor] {
            dfs(graph, *neighbor, visited);
        }
    }
}

medium

A. Change if visited[*neighbor] to if !visited[*neighbor]

B. Change visited[node] = true to visited[node] = false

C. Remove the for loop and call dfs only once

D. Change neighbor to node inside the loop

Solution

1. Step 1: Analyze the condition for recursive DFS call

   The code calls dfs only if visited[*neighbor] is true, meaning already visited nodes are revisited, causing infinite recursion.

2. Step 2: Correct the condition to avoid revisiting

   Change condition to if !visited[*neighbor] to visit only unvisited neighbors.

3. Final Answer:

   Change if visited[*neighbor] to if !visited[*neighbor] -> Option A

4. Quick Check:

   Visit unvisited neighbors only [OK]

Hint: Call DFS only on unvisited neighbors [OK]

Common Mistakes:

• Calling DFS on visited nodes causing infinite loops
• Incorrectly marking nodes as unvisited
• Removing necessary loops

5. Given a graph with possible cycles, how can you modify DFS in Rust to detect if the graph contains a cycle?

hard

A. Use BFS instead of DFS to detect cycles

B. Only mark nodes visited after all neighbors are visited

C. Ignore visited nodes and continue traversal

D. Use a recursion stack (call stack) boolean vector to track nodes in the current path and detect back edges

Solution

1. Step 1: Understand cycle detection in DFS

   To detect cycles, track nodes currently in recursion stack to find back edges indicating cycles.

2. Step 2: Implement recursion stack tracking

   Use a boolean vector to mark nodes in current DFS path; if a neighbor is in this stack, a cycle exists.

3. Step 3: Other options are incorrect

   Marking visited after neighbors or using BFS won't detect cycles reliably; ignoring visited nodes causes infinite loops.

4. Final Answer:

   Use a recursion stack (call stack) boolean vector to track nodes in the current path and detect back edges -> Option D

5. Quick Check:

   Recursion stack tracks cycles in DFS [OK]

Hint: Track recursion stack to find cycles in DFS [OK]

Common Mistakes:

• Not tracking recursion stack causing missed cycles
• Using BFS which needs extra logic for cycles
• Ignoring visited nodes causing infinite loops